Application Information Advanced On-chip Linearization in the A1332 Angle Sensor IC

Transcription

1 Application Information Advanced On-chip Linearization in the A Angle Sensor IC By Alihusain Sirohiwala and Wade Bussing Introduction Numerous applications in industries spanning from industrial automation and robotics, to electronic power steering and motor position sensing require monitoring the angle of a rotating shaft either in an on-axis or off-axis arrangement. The design of any successful angle measurement system for the above applications needs to be based on the needs of the particular application. These include: arrangement (off-axis or on-axis), air- gap, accuracy, and temperature range, among others. Degrees roughly an 6X improvement. This linearization can be performed based on data from a single rotation of the target magnet around the angle sensor IC. The angle readings from this rotation are used to generate linearization coefficients which can then be stored into on-chip EEPROM, optimizing that angle sensor IC, for that magnetic system. Allegro can provide the necessary software and/or DLLs to help customers program these devices at their end-of-line. A magnetic angle measurement system has two main sources of error: Sensor IC related errors:. intrinsic non-linearity;. parametric temperature drift;. noise. Magnetic input related errors:. field strength variation;. field non-linearity. Each Allegro angle sensor IC is tested and calibrated during production at Allegro using a homogenous magnetic field. As a result, intrinsic IC nonlinearity and temperature drift are reduced to a minimum before the angle sensor IC is shipped to customers. Please refer to product data sheets for temperature drift information. When using a magnet in a design, the magnetic input will most likely not be homogenous over the entire range of rotation it will have inherent errors. These magnetic input errors cause measurement error in the system. These factors become especially important when considering side-shaft or off-axis designs that have higher intrinsic magnetic errors. Even the most accurately calibrated angle sensor IC will produce inaccurate results if the error contribution from the magnetic input dominates. In most cases, even on-axis magnetic designs suffer from relatively large misalignments that occur during the assembly of the customer module in the production line. These magnetic error sources are inevitable and mitigating them is often impossible and almost always expensive. The approach of the Allegro A angle sensor IC is to solve this problem by using advanced linearization techniques to compensate for these errors at the customer s end-of-line manufacturing location. This document shows how magnetic input related errors in excess of ± degrees can be linearized by the A to as low as ±. Linearization Options There are two linearization techniques offered in the A angle sensor IC. The first is called Segmented Linearization, and the second is called Harmonic Linearization. Segmented Linearization is a programmable feature that allows adjustment of the transfer characteristic of the angle sensor IC such that linear changes in the applied magnetic field vector angle can be output as corresponding linear angle increments by the angle sensor IC. It is performed on the data collected from one rotation of the magnet around the angle sensor IC. On the other hand, Harmonic Linearization applies linearization in the form of correction harmonics whose phase and amplitude are determined by means of an FFT (Fast Fourier Transform) performed on the data collected from one rotation of the magnet around the angle sensor IC. Both of these techniques can be readily implemented using Allegro provided software to calculate coefficients and program on-chip EEPROM. Contact your local Allegro Representative to obtain the latest DLLs, software GUIs, and programming hardware. N Figure : Off-Axis (left) and On-Axis (right) S 69-AN

2 Definitions AIR-GAP Two different air-gap definitions can be used when talking about magnetic field sensors: package air-gap and crystal air-gap. PACKAGE AIR-GAP Package air-gap is defined as the distance between the nearest edge of the sensor housing and the nearest face/tangent-plane of the magnet. CRYSTAL AIR-GAP Crystal air-gap is defined as distance between the sensing element in the sensor housing and the nearest face of the magnet. To illustrate this difference, Figure shows both the crystal air-gap (4. mm) and package air-gap (.86 mm) for an A angle sensor IC and magnet in a side-shaft or off-axis configuration. In this document, the term air-gap always refers to the package air-gap, unless otherwise stated. The sensing elements are.6 mm below the top surface of the package. The distance between the sensing element center and the closest short edge of the package is.64 mm. 4. mm.86 mm ACCURACY ERROR Further down in this document, the angle error is displayed as a function of misalignment. For that purpose, it is necessary to introduce a single angle error definition for a full rotation. The summarized angle error on one full rotation is defined as angular accuracy error, and it is calculated according to the following formula: Angle Accuracy Error = E E max min In other words, it is the amplitude of the deviation from a perfect straight line between and 6 degrees. It is important to distinguish between angle sensor IC related errors and magnetic input related errors. This document highlights how advanced features in the A angle sensor IC can be used to compensate for magnetic input related errors. As far as angle sensor IC related errors are concerned, intrinsic non-linearity and parametric temperature drift are optimized for each Allegro angle sensor IC at Allegro s end-of-line test operation (see datasheet specifications for those parameters) before shipping to the customer. Noise performance can be optimized for the customer application by using on-chip filtering (see ORATE settings in A Programming Manual). Magnets In order to compare the performance of the Segmented or the Harmonic linearization options, both linearization techniques were performed on the same magnets. The magnets used were Neodymium N4 di-pole ring magnets available from Super Magnets. Figure 4 and Figure illustrate magnet dimensions. Figure : Crystal Air-gap versus Package Air-gap ANGLE ERROR Angle error is the difference between the actual position of the magnet and the position of the magnet as measured by the angle sensor IC. This measurement is done by reading the angle sensor IC output and comparing it with a high resolution encoder (refer to Figure ). E = a a Angle Error E [º] Sensor Real. mm 7. mm E max º E = a Sensor a Real E max Emin 6º Reference Angle a Real. mm E min Figure : Angle Error Definition Figure 4: Magnet R Dimensions Worcester, Massachusetts 6-6 U.S.A..8.8.;

3 . mm. mm Magnetic Field Strength (Gauss) 4 Magnet R R Linearized Point Magnet R R Linearized Point Table : Off Axis (Left) and On Axis (Right) Magnet Name R R. mm Figure : Magnet R Dimensions Manufacturer Super Magnets Super Magnets Inner Diameter Outer Diameter Height 7 mm mm mm mm mm mm Average Magnetic Field and Air-gap Dependency Material N4 Ni Plated N4 Ni Plated Package Air-gap X Axis (mm) Figure 6: Magnet Field Vector (Horizontal Component) Magnitude VS Air-gap As Measured by A, for Magnets R and R Magnet Error Analysis Using magnet R, an analysis was performed of the inherent non-linearity observed in the magnetic signal when measuring angle with a calibrated A under ideal alignment, as shown in Figure 7 and Figure mm The first step in the system design is to choose an appropriate magnet for the application air-gap. Usually the air-gap is in a range from to 4 mm. Figure shows the magnetic field as a function of air-gap for the magnets R and R. By default, many Allegro angle sensor ICs are trimmed to provide optimum performance at Gauss ( mt). In the case of the A, there is also a magnetic auto-scaling feature available upon request that dynamically adjusts internal gains to compensate for dynamic variations in air-gap. However, care should be taken with the magnetic design so that the air-gap variation does not result in fields that are too low (inadequate signal to noise ratio), or too high (saturation of signal-chain blocks), In general, a field strength of roughly G is ideal. Figure 7: Side-Shaft Arrangement with Magnet R Worcester, Massachusetts 6-6 U.S.A..8.8.;

4 4. mm Figure 8: Off Axis Arrangement, with Magnet R, Side- View Based on one rotation sampling the angle sensor IC output at equidistant angular points, we get the transfer characteristic as shown in Figure 9. Angle Output (Degrees) Magnet Error Figure 9: Angle Output with Target Magnet R Analyzing the above angle error in the frequency domain with an FFT, we get the error versus harmonics as shown below in Figure. Pk-Pk Amplitude of Harmonic Error (Degrees) Figure shows a similar analysis on magnet R. Pk-Pk Amplitude of Harmonic Error (Degrees) Harmonic Number Figure : Spectral Analysis of Angle Error using Magnet R Harmonic Number Figure : Spectral Analysis of Angle Error using Magnet R Worcester, Massachusetts 6-6 U.S.A..8.8.; 4

5 It is clear from the FFT data that most of the inherent error in both magnets R and R is from nd harmonic contributions, whereas st, 4 th, rd and higher harmonics are responsible for the remainder of the error. The root cause of this error is a mismatch in the amplitude of the radial (B r ) and tangential (B t ) components. The magnetic field vector, whose phase or angle is being measured by the angle sensor IC, can be expressed as two orthogonal components B r and B t as shown in Figure. 4. mm Magnetic Field Amplitude (Gauss) B Radial Component, Air-gap =.7 mm r B Tangential Component, Air-gap =.7 mm t -6 4 Angular Position (Degrees) B r B xy B t Figure : Radial (B r ) and Tangential (B t ) Components of the Field Ideally, these components should be identical in amplitude, and orthogonal in phase. Any deviation from this ideality introduces error in the resultant angle measurement. In ring magnets for side-shaft sensing, the mismatch in the radial and tangential component is inherent to the magnet design and manufacturing process and can vary depending on the manufacturer, and the manufacturing method. In the case of cylindrical magnets, the radial and tangential mismatch can be introduced by adding eccentricity or misalignment between the angle sensor IC and magnet. These mismatches result in an angle error profile with terms at multiple harmonics. Therefore, it is clear, that only correcting for the nd harmonic error term will not be sufficient, especially if high accuracy performance is required. Magnetic Field Amplitude (Gauss) Figure : Magnet R, Radial and Tangential Field Components B Radial Component, Air-gap = 4 mm r B Tangential Component, Air-gap = 4 mm t -6 4 Angular Position (Degrees) Figure 4: Magnet R, Radial and Tangential Field Components Worcester, Massachusetts 6-6 U.S.A..8.8.;

6 Segmented Linearization The A Segmented Linearization is a programmable feature that allows adjustment of the transfer characteristic of the device so that, changes in the applied magnetic field can be output as corresponding linear increments. Angle Output (Degrees) Un-Linearized Segmented Linearization Figure : Angle Output using R, Pre/Post Segmented Linearization Figure, above illustrates the angle output of the A both with and without the Segmented Linearization. In order to achieve this, an initial set of linearization coefficients has to be created. The user takes samples of angle: at every /6 interval of the full rotational range from to 6 degrees. The -reference point is set by the LIN_OFFSET EEPROM field. This becomes the zero-error point, and is therefore not represented in the coefficient table. Likewise, the 6-degree point is identical to the -reference point and is also not represented in the coefficient table. The rest of measured angles at the segment boundaries are placed in the LIN_COEFF... LIN_COEFF EEPROM fields. The following instructions describe the basic algorithm for applying these linearization coefficients. Sample implementations of this method are available through Allegro Customer Evaluation Software Tools. Figure shows the Angle output VS an Encoder reference both with and without Segmented Linearization applied. Figure 6 shows the Angle Error by subtracting the reference encoder value, both with and without Segmented Linearization applied. Figure 7 shows a zoomed in look at the Angle Error profile with Segmented Linearization applied. Steps for Implementing Segmented Linearization. Collect data Turn off all algorithmic processing except Segmented Linearization (SL), Angle Compensation (AC) and IIR filtering (FI), if these are desired ( FI and AC bits in CFG_, word 6, EEPROM bits +, SRAM bits 6+7, SL bit is in ). Turn on the Segmented Linearization Bypass bit (SB bit, word 6, EEPROM bit, SRAM bit ). This function can be used to take the measurements required for segmented linearization without having to otherwise pre-program the linearization table to a straight line. Find the desired zero-reference point, realizing that the linearly interpolated segments will be +., +4. etc. from this reference point. For side-shaft, picking a point where the error is at a peak or valley is optimal. The angle sensor IC reading at that point will be entered into the LIN_OFFSET coefficient in the next step. Move the encoder in the direction of increasing angle position. If the sensor angle output does not also increase, then either set the LR bit to reverse the direction of the angle sensor IC, or rotate the encoder in opposite direction for this calibration step. (In which case the post-linearization rotate bit (RO) will likely need to be set after calibration is complete). See A programming reference for more details. Move in encoder steps of. degrees and read angle sets. This process will produce the LIN_COEFF coefficients.. Program Coefficients Program LIN_OFFSET after multiplying with * (496/6), written in HEX after rescale. Program each of LIN_COEFF after multiplying with * (496/6), written in HEX after rescale.. Enable Linearization Set EEPROM bit SB=, since we now no longer need to bypass the linearization function (data collection in step is already completed). Set EEPROM bit SL = (note: it should already be set to from step ), to enable segmented linearization. The angle sensor IC output should now linearly interpolate along each segment and produce a corrected angle output. Results Figure 6 illustrates the segmented linearization performance in the form of angle error compared to a known-good encoder angle reference. Worcester, Massachusetts 6-6 U.S.A..8.8.; 6

7 Angle Error (Degrees) Figure 6: Angle Error using R, Pre/Post Segmented Linearization Although accurate as shown, Figure 6 is not a very insightful depiction of the true angle error performance. It only shows the angle error at the points in the transfer function where the postlinearization error is the least. If we were to measure the same device again, with a much smaller angle step between samples, we get what is shown in Figure 7. Notice the lobes of error between successive linearization points. These are expected since in each segment, the error is approximated as a straight line, when in fact it is sinusoidal. Given this type of sinusoidal input error pattern, Figure 7 is about the best performance one can achieve with a segmented approach using 6 segments. The segmented linearization implemented in the A only allows for this 6-segment linearization. The performance of this method Angle Error (Degrees) Un-Linearized Segmented Linearization 64 Sample Point 6 Sample Point Figure 7: Angle Error using R, Finer Sample Resolution, Segmented Linearization could conceivably be improved by either increasing the number of segments or by making the segment length variable, so that finer segments can be used for areas with higher curvature. However, both these enhancements result in higher processing time, and complexity. Harmonic Linearization As seen in the section analyzing errors from magnets R and R, it is clear that these errors are sinusoidal in nature, meaning that they can usually be well described by constituent harmonics of appropriate phase and amplitude. Harmonic Linearization takes advantage of this property and applies the linearization in the form of Harmonics whose phase and amplitude are determined by means of an FFT (Fast Fourier Transform) performed on the data collected from one rotation of the magnet around the angle sensor IC at the customer s end-of-line. Angle Output (Degrees) No Linearization With Harmonic Linearization Figure 8: Angle Output using R, Pre/Post Harmonic Linearization There is a great deal of flexibility built into the Harmonic Linearization function. The value of the individual harmonic Amplitudes and Phases are stored in -bit EEPROM fields for each of harmonics. The number of harmonics that need to be applied in a linearization can be specified by the user using the 4-bit HAR_MAX EEPROM field. This setting determines how many individual harmonic components (from to ) are used for computing harmonic linearization. (The Adv fields are used to determine which harmonics are applied for each component.) The -bit Field Adv field sets the increment between sequential pairs of applied harmonic components. The value entered, n (in the range to ), indicates how many harmonics to be skipped from the previous component to the current component. The count is applied as + n. For example, the first component Worcester, Massachusetts 6-6 U.S.A..8.8.; 7

8 (xc) minimum (n = ) is the st harmonic and the maximum (n = ) is the 4th harmonic. The effect is cumulative; when all components are set to n =, the 6th harmonic is available at the fifteenth component (xa). As an example, we use magnet R in a side-shaft configuration in order to linearize an A. In addition to enabling side-shaft applications, the flexibility built into this linearization method is also very useful in removing static misalignment errors at the customer s end-of-line. Steps for Implementing Harmonic Linearization. Collect data Turn off all algorithmic processing except temperature compensation and IIR filtering, if these are desired (FI and TC bits in CFG_, word 6, EEPROM bits +, SRAM bits 6+7). Move the encoder in the direction of increasing angle position. If the angle sensor IC does not also increase, then either set the LR bit to reverse the direction of the angle sensor IC, or rotate the encoder in opposite direction for calibration (in which case the post-linearization rotate bit (RO) will likely need to be set). See A programming reference for more details. Move in encoder steps such that the resultant data is a power of. Usually,, or 64 evenly spaced data points are sufficient.. Program Coefficients Perform an FFT on the measured data and then program, HARMONIC_AMPLITUDE, HARMONIC_PHASE, ADV, and HAR_MAX fields based the preferred implementation. A sample implementation of these features is available from your Allegro representative.. Enable Linearization Set EEPROM bit HL= to enable Harmonic linearization. The sensor output should now produce a corrected angle output. Results Figure 9 shows Harmonic Linearization performance for magnet R, with HARMAX = through. (And all ADV fields = ). In other words, this shows the performance as Harmonic correction is incrementally applied from the st up to the th harmonic. The same result is summarized in Figure to show the pk-pk angle error (on the y axis) versus the number of correction harmonics applied. The sharp drop in Angle error after the nd Angle Error (Degrees) Pk-Pk Angle Error (Degrees) No Harmonics Harmonic Harmonics Harmonics 4 Harmonics Harmonics 6 Harmonics 7 Harmonics 8 Harmonics 9 Harmonics Harmonics Harmonics Harmonics Harmonics 4 Harmonics Harmonics Figure 9: Post Harmonic Linearization Angle Error with HARMAX = ( to ), using R Number of Harmonics Figure : Linearized Angle Error VS Number of Harmonics Applied, using R harmonic correction is expected since the majority of the spectral error content resides in the nd harmonic (see section analyzing magnetic errors). In order to further investigate the error performance with harmonic linearization applied, especially when using small angular steps, the same device was re-measured several times, with finer angle steps (higher resolution) with each run. The data shows no underlying higher error regions. The post-linearization error is Worcester, Massachusetts 6-6 U.S.A..8.8.; 8

9 Angle Error (Degrees) Figure : Angle Error using R, Finer Sample Resolution, And Harmonic Linearization sub-. degrees. Number of Harmonics Used Angle Latency Considerations 6 Sample Points Sample Points 64 Sample Points 8 Sample Points Both Segmented and Harmonic linearization techniques are well suited for on-axis and off-axis magnetic applications. While segmented linearization divides the magnetic range into smaller sections which are linearized in a piece-wise fashion, harmonic linearization allows for a sinusoidal-based compensation of the error signal, which helps remove the high harmonic error content in misaligned as well as side-shaft arrangements. The added performance from harmonic linearization comes at the cost of higher computation time. The Figure describes the added latency to the angle measurement, from each additional harmonic that is added to the harmonic linearization. For example, based on the data in Figure, it is clear that to achieve < degree we need at- least 7 harmonics of correction. Now, when we look at the added latency in processing time associated with 7 harmonics in Figure, we see that it is µs. This means that every angle sample will take an additional µs to process. In contrast, the segmented linearization requires an additional computation time of µs. Therefore, for this particular magnet, the improved error performance of harmonic linearization comes at a cost of an additional µs of latency. For many applications the additional latency will not be a problem. As an example, in typical Electronic Power Steering (EPS) system hand-wheel angle sensor ICs, a new Angle value is requested every ms, meaning that there is more than enough time to perform even harmonics of linearization. Also, a lot of systems will avail of the ORATE feature of the A in order to reduce the noise-floor of the angle measurement by over-sampling. This will also inherently provide enough time to perform linearization functions without added latency since the additional averaging with allow for more time to Added Latency (µs) Figure : Added Angle Latency VS Number of Harmonics Used be budgeted for linearization operations. Effect of XYZ Misalignment on Linearized Angle Sensor IC In this section, we analyze the performance of an angle sensor IC that has been linearized for magnets R and R, and then mapped for misalignment errors in the X, Y and Z axes as shown in Figure. In the case of both magnets R and R, we use an initial starting position at X (air-gap) =.7 mm and 4 mm respectively, with Y, Z = mm, such that the angle sensor IC is positioned in the middle of the magnet height. We use this position as our Cartesian origin, and map misalignment performance from this reference according to the Table. Table : Mapping Range and Linearization Points for both Magnets R and R Magnet R Axes Min (mm) Linearization Point (mm) Max (mm) X (Air-gap) Y (Lateral) -... Z (Vertical) -... Magnet R Axes Min (mm) Linearization Point (mm) Max (mm) X (Air-gap) Y (Lateral) -... Worcester, Massachusetts 6-6 U.S.A..8.8.; 9

10 Angle Error in Degrees Magnet R Axes Z-Axis Vertical Misalignment Min (mm) Y-Axis Lateral Misalignment X-Axis Air Gap Figure : Definition of X, Y and Z Mapping Axes Air-gap - X Axis, in mm Linearization Point (mm) Magnet R R Linearized Point Magnet R R Linearized Point Figure 4: Angle Error VS Air-gap for Both Magnet R and R Max (mm) Z (Vertical) -... The angle error performance for both Magnets R and R, as a function of air-gap (X axis) is illustrated in Figure 4. A few observations can be made by studying the plot in Figure 4. From the value of the angle error at the linearization point (denoted by the red circle) it is clear that the angle sensor IC is able to achieve very similar post-linearization performance for both magnets. From that limited perspective, both magnets can be used to achieve identical performance. However, upon studying the shape of the error curves versus air-gap in Figure 4, it is clear that magnet R (black trace) has a steeper rise in error as the angle sensor IC is misaligned away from the linearization point (red circle), as compared to magnet R (blue trace) Vertical (Z) Missalignment (mm) Vertical (Z) Missalignment (mm) Lateral (Y) Misalignment (mm) Figure : Magnet R, Misalignment Performance (Vertical and Lateral Axes) at Air-gap =.7 mm Lateral (Y) Misalignment (mm) Figure 6: Magnet R, Misalignment Performance (Vertical and Lateral Axes) at Air-gap = 4 mm Worcester, Massachusetts 6-6 U.S.A..8.8.;

11 As an example, increasing the air-gap between the angle sensor IC and magnet R by mm, results in the about the same performance degradation, as increasing the air-gap between the same angle sensor IC and magnet R by 4 mm. The better air-gap performance of magnet R can be attributed to the fact that it is a thicker ring magnet ( mm thick) as compared to R ( mm thick). In a similar fashion, we can analyze the misalignment performance in both the lateral and vertical (Y and Z) axes, by comparing the two filled contour plots for magnets R and R, shown in Figure and Figure 6 respectively. These plots have been generated by using the data from lab measurements mapping the performance at each point in space. For both these plots, the origin (Y =, Z = ) position represents the performance at the linearized point (the same as the red dots in Figure 4). As the angle sensor IC is misaligned from this origin, the angle error observed at each point is placed in a color bin according to the legend shown. The numbers on the legend represent degrees of peak error. As an example, the white region in the middle of each plot denotes the area for which the angle error performance remains below ± degree. Similarly, the brown areas in each plot denote regions where the angle error is greater than ±7 degrees. Looking at the two contour plots, it is clear that for the same misalignment in Y and Z, the angle sensor IC + magnet R combination result is lower angle error increase, as compared to angle sensor IC + magnet R. As an example, the white area for which the angle error is less than ± degree is.669 mm for magnet R while it is. mm for magnet R. Additionally, it is clear that the white area is vertically elongated for the case of R, as compared to R. This makes sense considering that the vertical height of ring magnet R ( mm) is greater than that of ring magnet R ( mm). These contours show the dependence of angle error performance, on magnet geometry. Conclusion There are many factors involved in a successful angle sensing application. Minimizing angle error over temperature, positional misalignment, and air-gap, is key. These variables are very related to system level design choices like magnet geometry, magnet arrangement (on-axis or off-axis), magnetic material, and mechanical tolerances. As such, flexibility is required of the angle sensor IC, in order to work around these potential error sources without adding complexity and cost to the system-level design. Even the best magnetic angle sensor IC is only as good as the magnetic field that is senses. On-Chip, programmable, and customizable linearization, as implemented in the A angle sensor IC, allows the system designer to meet the aforementioned accuracy objectives without adding additional complexity and cost to the system design. The A offers two linearization options - segmented and harmonic. Both these options were studied using reference magnets R and R. The results showed that though segmented linearization achieves faster processing times, it is limited in its ability to correct for sinusoidal error terms. In that regard, the harmonic linearization performs better. Additionally, the flexibility in the harmonic linearization, particularly the ability to change the number of correction harmonics used, allows the used to achieve the optimal trade-off between computation time and error performance. For both magnets R and R, it was seen that ± degrees of angle error can be brought to within ±. degrees with linearization applied. Lastly, using the mapping technique, the effect of mechanical misalignment of the linearized angle sensor IC was studied. It was seen that a taller ring magnet translates into better tolerance to vertical misalignments, whereas a thicker ring magnet translates into better tolerance to changes in Air-gap. Whatever the angle sensing challenges faced by the system- level designer, a combination of appropriate magnetic design and advanced on-chip linearization in the Allegro A can help achieve the desired performance while minimizing added complexity and cost. Worcester, Massachusetts 6-6 U.S.A..8.8.;

12 Revision History Revision Current Revision Date January, Initial Release Description of Revision Copyright, The information contained in this document does not constitute any representation, warranty, assurance, guaranty, or inducement by Allegro to the customer with respect to the subject matter of this document. The information being provided does not guarantee that a process based on this information will be reliable, or that Allegro has explored all of the possible failure modes. It is the customer s responsibility to do sufficient qualification testing of the final product to insure that it is reliable and meets all design requirements. For the latest version of this document, visit our website: Worcester, Massachusetts 6-6 U.S.A..8.8.;